JEE Main 2014MathematicsApplication of DerivativesMediumMCQ

JEE Main 2014 — Application of Derivatives Question with Solution

JEE Main 2014 (06 Apr)

Question

If f& g are differentiable functions in [0, 1] satisfying f0=2=g1, g0=0 & f1=6,  then for some c∈]0, 1[ 

Choose an option

Show full solutionCorrect option: B
Correct answer
Bf'c=2g'c

Step-by-step explanation

Let hx=fx-2gx clearly h0=h1

Also hx is continuous and differentiable.

Hence hx satisfy all conditions of Rolle's theorem in 0, 1. According to Rolle's theorem there exist atleast one c∈0, 1 such that h'x=0⇒f'x-2g'x=0

⇒f'c=2g'c.

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About this question

This is a previous-year question from JEE Main 2014, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.